Isolating the decay rate of cosmological gravitational potential

The decay rate of cosmological gravitational potential measures the deviation from Einstein-de Sitter universe and can put strong constraints on the nature of dark energy and gravity. Usual method to measure this decay rate is through the integrated Sachs-Wolfe (ISW) effect-large scale structure (LSS) cross correlation. However, the interpretation of the measured correlation signal is complicated by the galaxy bias and matter power spectrum. This could bias and/or degrade its constraints to the nature of dark energy and gravity. But, combining the lensing-LSS cross correlation measurements, the decay rate of gravitational potential can be isolated. For any given narrow redshift bin of LSS, the ratio of the two cross correlations directly measures $[d\ln D_{\phi}/d\ln a]H(z)/W(\chi,\chi_s)$, where $D_{\phi}$ is the linear growth factor of the gravitational potential, $H$ is the Hubble constant at redshift $z$, $W(\chi,\chi_s)$ is the lensing kernel and $\chi$ and $\chi_s$ are the comoving angular diameter distance to lens and source, respectively. This method is optimal in the sense that (1) the measured quantity is essentially free of systematic errors and is only limited by cosmic variance and (2) the measured quantity only depends on several cosmological parameters and can be predicted from first principles unambiguously. Though fundamentally limited by inevitably large cosmic variance associated with the ISW measurements, it can still put useful independent constraints on the amount of dark energy and its equation of state. It can also provide a powerful test of modified gravity and can distinguish the Dvali-Gabadadze-Porrati model from $\Lambda$CDM at $>2.5\sigma$ confidence level.Comment: 5 pages, 3 figures. Accepted to ApJ. Added more discussions and presented more detailed explanation of a key formula used in the pape

Confirmation of the Copernican principle at Gpc radial scale and above from the kinetic Sunyaev Zel'dovich effect power spectrum

The Copernican principle, a cornerstone of modern cosmology, remains largely unproven at Gpc radial scale and above. Here we will show that, violations of this type will inevitably cause a first order anisotropic kinetic Sunyaev Zel'dovich (kSZ) effect. If large scale radial inhomogeneities have amplitude large enough to explain the "dark energy" phenomena, the induced kSZ power spectrum will be much larger than the ACT/SPT upper limit. This single test confirms the Copernican principle and rules out the adiabatic void model as a viable alternative to dark energy.Comment: 4 pages, 2 figures. v2: updated with ACT result. v3: updated with SPT result. Expanded discussions. Accepted to PR

Non-negative matrix factorization for self-calibration of photometric redshift scatter in weak lensing surveys

Photo-z error is one of the major sources of systematics degrading the accuracy of weak lensing cosmological inferences. Zhang et al. (2010) proposed a self-calibration method combining galaxy-galaxy correlations and galaxy-shear correlations between different photo-z bins. Fisher matrix analysis shows that it can determine the rate of photo-z outliers at a level of 0.01-1% merely using photometric data and do not rely on any prior knowledge. In this paper, we develop a new algorithm to implement this method by solving a constrained nonlinear optimization problem arising in the self-calibration process. Based on the techniques of fixed-point iteration and non-negative matrix factorization, the proposed algorithm can efficiently and robustly reconstruct the scattering probabilities between the true-z and photo-z bins. The algorithm has been tested extensively by applying it to mock data from simulated stage IV weak lensing projects. We find that the algorithm provides a successful recovery of the scatter rates at the level of 0.01-1%, and the true mean redshifts of photo-z bins at the level of 0.001, which may satisfy the requirements in future lensing surveys.Comment: 12 pages, 6 figures. Accepted for publication in ApJ. Updated to match the published versio

Testing eternal inflation with the kinetic Sunyaev Zel'dovich effect

Perhaps the most controversial idea in modern cosmology is that our observable universe is contained within one bubble among many, all inhabiting the eternally inflating multiverse. One of the few way to test this idea is to look for evidence of the relic inhomogeneities left by the collisions between other bubbles and our own. Such relic inhomogeneities induces a coherent bulk flow over gigaparsec scales. Therefore, bubble collisions leave unique imprints in the cosmic microwave background (CMB) through the kinetic Sunyaev Zel'dovich (kSZ) effect, temperature anisotropies induced by the scattering of photons from coherently moving free electrons in the diffuse intergalactic medium. The kSZ signature produced by bubble collisions has a unique directional dependence and is tightly correlated with the galaxy distribution; it can therefore be distinguished from other contributions to the CMB anisotropies. An important advantage of the kSZ signature is that it peaks on arcminute angular scales, where the limiting factors in making a detection are instrumental noise and foreground subtraction. This is in contrast to the collision signature in the primary CMB, which peaks on angular scales much larger than one degree, and whose detection is therefore limited by cosmic variance. In this paper, we examine the prospects for probing the inhomogeneities left by bubble collisions using the kSZ effect. We provide a forecast for detection using cross-correlations between CMB and galaxy surveys, finding that the detectability using the kSZ effect can be competitive with constraints from CMB temperature and polarization data.Comment: 33 pages, 17 figures. Minor clarifications added in version 2, conclusions are unchange

Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect

A generic prediction of general relativity is that the cosmological linear density growth factor $D$ is scale independent. But in general, modified gravities do not preserve this signature. A scale dependent $D$ can cause time variation in gravitational potential at high redshifts and provides a new cosmological test of gravity, through early time integrated Sachs-Wolfe (ISW) effect-large scale structure (LSS) cross correlation. We demonstrate the power of this test for a class of $f(R)$ gravity, with the form $f(R)=-\lambda_1 H_0^2\exp(-R/\lambda_2H_0^2)$. Such $f(R)$ gravity, even with degenerate expansion history to $\Lambda$CDM, can produce detectable ISW effect at z\ga 3 and l\ga 20. Null-detection of such effect would constrain $\lambda_2$ to be $\lambda_2>1000$ at $>95$ confidence level. On the other hand, robust detection of ISW-LSS cross correlation at high $z$ will severely challenge general relativity.Comment: 5 pages, 2 figures. Accepted to PRD. v2: Revised to address to more general audience. v3: added discussion